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arXiv · 1207.0080

A note on coloring line arrangements

Eyal Ackerman·Rom Pinchasi
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Abstract

We show that the lines of every arrangement of $n$ lines in the plane can be colored with $O(\sqrt{n/ \log n})$ colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. \cite{BCC12} by a $Θ(\sqrt{\log n})$ factor. Any further improvement on this bound will improve the best known lower bound on the following problem of Erdős: Estimate the maximum number of points in general position within a set of $n$ points containing no four collinear points.

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Eyal Ackerman, Rom Pinchasi. 2012-06-30. A note on coloring line arrangements. https://arxiv.org/abs/1207.0080

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